How are the Pythagorean Theorem and the distance formula different?

Pythagorean Theorem: In any right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Distance Formula: If the coordinates of two points in a plane are (x1, y1) and (x2, y2), then the distance between the two points is equal to .

How is similarity used in the proof of the Pythagorean Theorem?

Because the two new triangles each share an angle with the original one, their third angle must be (90°-the shared angle), so all three have an angle we will call α (In the original triangle: ∠BCA. And we can now use the relationship between sides in similar triangles, to algebraically prove the Pythagorean Theorem.

How is the Pythagorean Theorem related to the equation of a circle?

So now we have our Pythagorean Theorem equation: x^2 + y^2 = r^2. This is also the equation for a circle centered on the origin on the coordinate plane. [The more general equation for a circle with a center (a,b) is (x-a)^2 + (y-b)^2 = r^2.

What is the Pythagorean Theorem used for?

The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle. This theorem is an extremely useful tool that provides the basis for more complex trigonometry theories such as the converse of the Pythagorean theorem.

How does the Pythagorean Theorem help you find diagonal distance?

As per the property of rectangles the length and breadth (width) are at right angles(perpendicular) to each other. Keeping this property in mind, the diagonal can be found by applying the Pythagoras theorem , as the length , breadth and diagonal together form a right angled triangle(diagonal being the hypotenuse).

How can you use the Pythagorean Theorem to find the distance between two points on a coordinate plane?

Key Points

1. The Pythagorean theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides.
2. The distance, 𝑑 , between two points with coordinates ( 𝑥 , 𝑦 )   and ( 𝑥 , 𝑦 )   is given by 𝑑 =  ( 𝑥 − 𝑥 ) + ( 𝑦 − 𝑦 ) .

What is the equation used for the Pythagorean Theorem?

Pythagoras theorem equation helps you to solve right-angled triangle problems, using the Pythagoras equation: c2 = a2 + b2 (‘c’ = hypotenuse of the right triangle whereas ‘a’ and ‘b’ are the other two legs.). Hence, any triangle with one angle equal to 90 degrees will be able to produce a Pythagoras triangle.

What is the Pythagorean theorem in simple terms?

Definition of Pythagorean theorem : a theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.